Evaluate log base 3 of 8

Problem

(log_3)(8)

Solution

1. Apply the change of base formula to rewrite the expression using natural logarithms or common logarithms.

(log_b)(a)=ln(a)/ln(b)

2. Substitute the given values into the formula.

(log_3)(8)=ln(8)/ln(3)

3. Rewrite the number 8 as a power of 2 to simplify the expression further if needed.

8=2

4. Apply the power rule for logarithms, which states ln(xy)=y*ln(x)

ln(2)/ln(3)=(3*ln(2))/ln(3)

Final Answer

(log_3)(8)=(3*ln(2))/ln(3)

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